8272
J. Phys. Chem. B 1999, 103, 8272-8276
A Criterion for Evaluating the Thermal Stability of Glasses Kangguo Cheng Department of Materials Science and Engineering, and Beckman Institute for AdVanced Science and Technology, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801 ReceiVed: January 11, 1999; In Final Form: August 3, 1999
To evaluate the stability of glasses, a new criterion kf(T) ) ν exp[-E/RT‚(Tp - Tf)/Tf] is proposed, where Tf is the inflection point temperature and Tp is the maximum peak temperature on the differential thermal analysis curves. Not only the kinetic parameters of the crystallization of glasses, namely, activation energy, E, and frequency factor, ν, but also a thermodynamic factor (Tp - Tf)/Tf have been taken into account in the kf(T) criterion. A higher value of kf(T) means a poor stability of glasses. Two glasses with the compositions of Li2O‚2SiO2 and Li2O‚1.5SiO2 were prepared by the conventional melting process and the validity of the proposed criterion is ascertained by applying it on these glasses. The stability of these two glasses was also evaluated by the existing criteria. The results indicate that all existing criteria are either affected by the heating rate or they are not suitable for evaluating the stability of these glasses. On the contrary, the new criterion is independent of the heating rate and gives consistent results on the evaluation of the stability of Li2O-SiO2 glasses within a large temperature range. The Li2O‚1.5SiO2 glass is less stable than the Li2O‚2SiO2 glass.
1. Introduction In the past decades, glass and glass-ceramics have attracted much attention because of their unique properties, such as excellent chemical durability, amazing optical transparency, and excellent electrical properties. Besides the traditional silicate glass, numerous new glass systems have been developed under the demand of modern industrial applications.1-4 These glasses include phosphate glass,5,6 amorphous metal alloy7-9 and fluoride glass,10,11 etc. The critical issue for the existing or potential applications of these glasses is their thermal stability against crystallization. They should be stable against thermal aging during their application. On the other hand, those glasses that serve as the intermediate products for fabricating glassceramics are expected to possess an appropriate thermal stability. They should be sufficiently stable against devitrification when the liquid glasses are quenched, but they should not be too stable to form nuclei and subsequently grow to crystals when they are annealed to form glass-ceramics. Therefore, it is very important to evaluate the thermal stability of glasses against crystallization when they are subjected thermal aging during their application, or subjected to reheating on purpose during the fabrication of glass-ceramics. Dietzel12 introduced the first simple criterion, ∆T ) Tx - Tg, where Tx is the crystallization starting temperature and Tg is the glass transition temperature. Besides Tx and Tg, other characteristic temperatures, such as the maximum peak temperature, Tp, and the melting temperature, Tm, are also used to evaluate the stability of glasses.13-16 For example, Hruby15 proposed the Hr criterion, Hr ) (Tx - Tg)/(Tm - Tp). Two other criteria developed from the Hr criterion are H′ and S criteria, where H′ ) (Tx Tg)/Tg and S ) (Tp - Tx)(Tx - Tg)/Tg, respectively.16 Some authors17-19 suggested that the crystallization activation energy, E, could also be used to evaluate the glass stability, but criteria based on the activation energy do not always fit with the actual experimental observation in some glass systems.20 The crystallization rate constant, k(T) ) ν exp(-E/RT), takes into account both activation energy, E, and frequency factor, ν, so it was
believed to be a good criterion for the evaluation of the glass stability.20,21 Unfortunately, it was found later that the k(T) criterion is susceptible to the heating rate and temperature.22,23 It goes the opposite way when heating rates are changed. More recently, two modified k criteria were proposed. One is ky(T) ) ν exp[-E/RT‚(Tx - Tg)/Tm]22 and the other is kb(T) ) ν exp(-E/RT‚Hr).23 In this paper, a new criterion for evaluating the thermal stability of glasses is proposed and its validity is ascertained by applying it to Li2O-SiO2 glass systems. Comparisons are also made between the new criterion and the existing criteria. 2. Theoretical Analysis An isothermal transition of glasses can be described by the Johnson-Mehl-Avrami equation24-26 as
x ) 1 - exp[-(kt)n]
(1)
where x is the crystallized fraction of glasses; n is the Avrami exponent; k is the reaction rate constant, which is related to the activation energy, E, and frequency factor ν through the Arrhenius temperature dependence
k ) ν exp(-E/RT)
(2)
where R is the gas constant. Applying the Johnson-Mehl-Avrami equation to the nonisothermal transition of glasses, however, requires to take into account the dependence of k on time, t. Thus
x ) 1 - exp[-(
∫0tk(t)dt)n]
(3)
At a certain temperature, Tf, the crystallization rate of a glass, dx/dt reaches its maximum, i.e.,
d2 x |T)Tf ) 0 dt2
10.1021/jp990152k CCC: $18.00 © 1999 American Chemical Society Published on Web 09/09/1999
(4)
Thermal Stability of Glasses
J. Phys. Chem. B, Vol. 103, No. 39, 1999 8273 2 d2x Cg d2∆T β Cg d2∆T ) ) h dt2 h dT2 dt2
Equation 10 indicates that the crystallization rate, dx/dt, is proportional to the slopes of DTA curves, d∆T/dT. Correspondingly, eq 11 indicates that the crystallization rate, dx/dt, reaches its maximum at the inflection point temperature, Tf, on the DTA curves. Now it is clear that the temperature Tf in eq 5 is just the inflection point temperature on DTA curves. Since both the formation of glasses and their crystallization are the kinetic processes, it is reasonable to evaluate the thermal stability of glasses by the kinetic parameter, k(T). Furthermore, a thermodynamic factor, Tp - Tf, takes into account the strong dependence of the shape of a DTA curve on the heating rate. Therefore, a new criterion is finally defined as
Figure 1. Typical crystallization peak on a DTA curve.
By taking the second derivative of eq 3, combining it with eq 4, and following the procedure in ref 20, one can finally derive an equation relating the crystallization kinetics parameters of glasses to temperature, Tf, and heating rate, β
ln Tf /β ) E/RTf + ln E/R - ln ν 2
(11)
(5)
kf(T) ) ν exp[-E/RT‚(Tp - Tf)/Tf]
(12)
Similar to the existing k(T) criteria, the greater values of kf(T), the poorer the stability of glasses. 3. Experimental Procedures
since during a DTA run with the a constant heating rate, β, temperature, T, is related to time, t, by
dT ) βdt
(6)
Obviously a plot of ln(Tf2/β) versus 1/Tf would be linear and activation energy, E, and frequency factor, ν, can be easily determined from the slope and the interception of the plot. It should be noted that, however, so far we have not explained how to determine the temperature, Tf, from nonisothermal experiments. In duration of t ∼ t + dt, the temperature of the reference material increases from T to T + dT. Correspondingly, the temperature of glass samples increases from T + ∆T to T + ∆T + d∆T, as shown in Figure 1. Assume the crystallized fractions of a glass at t and t + dt are x and x + dx, respectively. Consideration of energy conservation yields
Cg[1 - (x + dx)]d∆T + Cc(x + dx)d∆T ) hdx
(7)
where Cg is the molar heat capacity of the base glass; Cc is the heat capacity of the crystallized glass; h is the molar enthalpy change of glass-crystal transition. The term of hdx on the righthand side of eq 7 represents the heat generation due to the crystallization of the glass with amount of dx. The sum on the left-hand side of eq 7 is the total heat required to cause a temperature increase of d∆T for the crystalline fraction, (x + dx), and the remaining glass, [1 - (x + dx)]. Rearrangement of eq 7 yields
[Cg + (Cc - Cg)x]d∆T ) hdx
(8)
For most glass systems, the difference between Cc and Cg is very small. Since x is always less than 1, (Cc - Cg)x is much less than Cg and therefore it can be neglected in eq 8. Thus,
Cgd∆T ) hdx
(9)
Derivatives of eq 9 yield
dx Cg d∆T βCg d∆T ) ) dt h dt h dT
(10)
Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses were employed for this investigation. It is well known that the Li2O-SiO2 glass system exhibits strong bulk crystallization. Analytical grade reagents of Li2CO3 and SiO2 were well mixed by ball-milling, and then melted in a platinum crucible at 1400 °C for 4 h. The liquid glasses were quenched by pouring them into a cold copper mold. The amorphous nature of the as-quenched glasses was confirmed by X-ray diffraction (XRD). Glass powders of 200 ( 5 mg with an average size of 90 µm were employed for each DTA run with the reference material of alumina. Temperature calibrations of the instrument were performed by using the well-determined melting temperature of high-purity indium. The heating rates were carefully selected from 2 °C/min to 20 °C/min because the DTA curves show appropriate shapes for data analyses. The maximum peak temperature, Tp, was determined directly from DTA curves. To determine the inflection point temperature, Tf, DTA curves were differentiated and thereby derivative differential thermal analysis (DDTA) curves were generated. Then the inflection point temperature, Tf, was determined as the peak temperature on DDTA curves. A minimum of five samples was employed for each isothermal and nonisothermal determination. 4. Result and Discussion The typical DTA and DDTA curves of Li2O‚2SiO2 and Li2O‚ 1.5SiO2 glasses at the heating rate of 10 °C/min are shown in Figure 2 and Figure 3, respectively. The glass transformation temperature, Tg, the crystallization starting temperature, Tx, the maximum peak temperature, Tp, and the melting point temperature, Tm, were directly determined from DTA curves. The inflection point temperature, Tf, was determined from the maximum peak temperature on the DDTA curve. All of these characteristic temperatures are summarized in Table 1. Apparently, all of the characteristic temperatures of the studied glasses increase with the increasing heating rates. The glass transition temperature, Tg, and the maximum peak temperature, Tp, decrease with the increase of the ratio of Li2O/ SiO2. In lithia-rich solid solutions, it is believed that the structure should consist of silicate sheets in which some of the constituent [SiO4] tetrahedra are replaced by [LiO4] tetrahedra; the sheets should be connected by the layers of lithium ions.27 For the
8274 J. Phys. Chem. B, Vol. 103, No. 39, 1999
Cheng
TABLE 1: Characteristic Parameters of Li2O‚2SiO2 and Li2O‚1.5SiO2 Glasses β/K‚min-1
Tg/°C
Tx/°C
Tp/°C
Tf/°C
Tm/°C
∆T/°C
Hr
H′
S
E/RTp
Li2O‚2SiO2
2 4 8 10 12 15 20
443 452 458 462 467 473 481
530 541 556 561 567 574 582
587 602 619 626 633 640 647
560 574 590 596 603 609 616
1020 1024 1027 1031 1033 1037 1042
87 89 98 99 100 101 101
0.201 0.211 0.240 0.244 0.250 0.254 0.256
0.122 0.123 0.134 0.135 0.135 0.135 0.134
6.93 7.49 8.45 8.76 8.92 8.94 8.71
32.7 32.2 31.6 31.3 31.1 30.8 30.6
Li2O‚1.5SiO2
2 4 8 10 12 15 20
425 433 440 444 449 454 460
514 527 539 545 551 557 564
569 584 599 606 610 616 623
543 557 571 577 581 586 593
1126 1130 1135 1139 1143 1147 1152
89 94 99 101 102 103 104
0.160 0.172 0.185 0.189 0.191 0.194 0.197
0.128 0.133 0.139 0.141 0.141 0.142 0.142
7.01 7.59 8.33 8.59 8.34 8.36 8.37
33.4 32.9 32.3 32.0 31.9 31.7 31.4
glass
Figure 2. DTA curves of Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses at various heating rates.
Figure 4. Plots of ln(Tf2/β) versus 1/Tf.
TABLE 2: Least-Square Fitting to Evaluate the Plots of ln(Tf 2/β) vs 1/Tf glass
ln(Tf 2/β)
Li2O‚2SiO2 Li2O‚1.5SiO2
28159/Tf - 21.11 30889/Tf - 25.16
a
Figure 3. DDTA curves of Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses at various heating rates.
Li2O‚1.5SiO2 glass which contains 60 mol % SiO2, its composition is beyond the range where complete Li2O‚2SiO2 solid solution can be found, more lithium ions are expected to be at the interstitial sites of the network as glass modifier, which contributes the decrease of Tg and Tp. The melting point temperature, Tm, of the Li2O‚1.5SiO2 glass is higher than that of Li2O‚sSiO2 because its composition deviates from the stoichiometry of Li2O‚2SiO2.19 To determine the kinetic parameters of the crystallization, the plot of ln(Tf2/β) versus 1/Tf is given in Figure 4. On the basis of eq 5, the activation energy, E, and the frequency factor,
E/kJ‚mol-1
ν/s-1
ra
234 257
6.9 × 4.3 × 1013
0.9974 0.9996
1011
r is the correlation coefficient.
ν, are evaluated by the least-squares fitting method. The results of the calculations are summarized in Table 2. The existing stability criterion parameters based on these characteristic temperatures are also listed in Table 1. The greater these parameters, the more stable the glass should be. Branda et al. suggested that E/RTp could also be used to evaluate the stability of glasses. Higher values of E/RTp imply greater devitrification tendency. According to E/RTp criterion, glass Li2O‚2SiO2 is more stable than glass Li2O‚1.5SiO2, which is consistent with the evaluation of the Hr criterion. On the contrary, ∆T and H′ criteria indicate that glass Li2O‚1.5SiO2 is more stable than glass Li2O‚2SiO2. The S criterion fails to evaluate the stability of these two glasses because it is not selfconsistent, i.e., it gives contrary evaluations at the different heating rates. As discussed above, more lithium ions act as the network modifier in Li2O‚1.5SiO2 glass than in Li2O‚2SiO2 glass, so Li2O‚1.5SiO2 glass should be easier to devitrify and therefore it should be less stable. As shown in Table 1, the values of ∆T, H′, and S for the studied glasses are rather close and susceptible to the heating rate, so any error in determining the characteristic temperatures would have resulted in opposite evaluation on the stability of the glasses. The E/RTp criterion fits with the experimental observation. However, as shown in Table 1, the values of E/RTp for the studied two glasses are
Thermal Stability of Glasses
J. Phys. Chem. B, Vol. 103, No. 39, 1999 8275
TABLE 3: Kinetic Parameters k(T), ky(T), kb(T), and kf(T) for Li2O‚2SiO2 and Li2O‚1.5SiO2 Glasses β/K‚min-1
k(Tp)/s-1
Ky(Tp)/s-1
kb(Tp)/s-1
kf(Tp)/s-1
kf(Tf)/s-1
kf(Tg)/s-1
Li2O‚2SiO2
2 4 8 10 12 15 20
-3
4.16 × 10 7.29 × 10-3 1.35 × 10-2 1.72 × 10-2 2.19 × 10-2 2.78 × 10-2 3.52 × 10-2
7.62 × 10 7.58 × 1010 6.39 × 1010 6.40 × 1010 6.39 × 1010 6.40 × 1010 6.56 × 1010
9.59 × 10 7.78 × 108 3.51 × 108 3.26 × 108 2.91 × 108 2.70 × 108 2.75 × 108
11
2.39 × 10 2.38 × 1011 2.39 × 1011 2.34 × 1011 2.38 × 1011 2.33 × 1011 2.37 × 1011
11
1.93 × 10 1.91 × 1011 1.89 × 1011 1.84 × 1011 1.88 × 1011 1.83 × 1011 1.88 × 1011
2.31 × 1011 2.30 × 1011 2.31 × 1011 2.25 × 1011 2.29 × 1011 2.25 × 1011 2.29 × 1011
Li2O‚1.5SiO2
2 4 8 10 12 15 20
5.03 × 10-3 9.55 × 10-3 1.78 × 10-2 2.35 × 10-2 2.76 × 10-2 3.50 × 10-2 4.59 × 10-2
4.19 × 1012 3.84 × 1012 3.56 × 1012 3.48 × 1012 3.46 × 1012 3.46 × 1012 3.47 × 1012
1.22 × 1011 8.68 × 1010 6.19 × 1010 5.51 × 1010 5.32 × 1010 5.09 × 1010 4.90 × 1010
1.34 × 1013 1.33 × 1013 1.33 × 1013 1.30 × 1013 1.31 × 1013 1.28 × 1013 1.30 × 1013
1.05 × 1013 1.04 × 1013 1.02 × 1013 0.99 × 1013 1.01 × 1013 0.98 × 1013 1.00 × 1013
1.29 × 1013 1.28 × 1013 1.28 × 1013 1.25 × 1013 1.26 × 1013 1.23 × 1013 1.25 × 1013
glass
10
Figure 5. Susceptibility of kb(T), kb(T), and kf(T) on the heating rate of Li2O‚2SiO2.
also very close. Extreme accuracy in determining the vaules of E and Tp is required for correct evaluations. Otherwise, contrary evaluation could have been given by E/RTp criterion. Criteria based on the crystallization rate constant, k, have also been proposed to evaluate the thermal stability of glasses. The greater the values of k, the poorer stability of glasses. The values of k(T), ky(T), kb(T), and kf(T) criteria for Li2O‚2SiO2 and Li2O‚ 1.5SiO2 glasses are calculated and listed in Table 3. All of these criteria indicate that Li2O‚2SiO2 is more stable than Li2O‚ 1.5SiO2, which is consistent with the evaluation of the Hr criterion and experimental observation. It should be noted that k(T) is much more significantly affected by the heating rate than ky(T), kb(T), and kf(T) criteria. Its values can vary one order in magnitude as the heating rates vary from 2 °C/min to 20 °C/ min. For a further comparison of the dependence of ky(T), kb(T), and kf(T) on the heating rate, the ratios of the changes of ky(T), kb(T), and kf(T) values at various heating rates to those values at the heating rate of 2 °C/min are shown in Figure 5 and Figure 6 for Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses, respectively. It is clearly shown that kf(T) is almost constant at various heating rates, while ky(T) and kb(T) changes with the heating rates. Comparison of values of kf(T) within a large temperature ranges for Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses is made at various heating rates and is shown in Figure 7. Again, for each glass, its kf(T) curves at various heating rates overlap, which verifies that kf(T) is less affected by the heating rate. At a given temperature, the values of kf(T) for Li2O‚2SiO2 glass are much lower than that of Li2O‚1.5SiO2 glass, so the former is much more stable than the latter.
8
Figure 6. Susceptibility of ky(T), kb(T), and kf(T) on the heating rate of Li2O‚1.5SiO2.
Figure 7. Plots of kf(T) versus T at various heating rates to verify the stable order.
5. Conclusions A new criterion kf(T) has been proposed for evaluating the stability of glasses from DTA data. Not only the crystallization kinetic parameters such as activation energy, E, and frequency factor, ν, but also a thermodynamic factor (Tp - Tf)/Tf are taken into account in the kf(T) criterion. A higher value of kf(T) indicates a poorer stability of glasses. The validity of the criterion is ascertained by applying it to evaluate the stability of Li2O‚2SiO2 and Li2O‚1.5SiO2 glasses. It is shown that the new criterion kf(T) is almost independent of the heating rate. It can be used to evaluate the thermal stability of glasses in a large range of temperature, while the existing criteria are either
8276 J. Phys. Chem. B, Vol. 103, No. 39, 1999 affected by the heating rate or they are not suitable for evaluating the stability of these glasses at all. Finally, it is verified that the Li2O‚1.5SiO2 glass is less stable than the Li2O‚2SiO2 glass. References and Notes (1) Wong-Ng, W.; Freiman, S. W. Appl. Supercond. 1994, 2, 163180. (2) Rawson, H. IEE Proceedings-A-Sci. Measur. Technol. 1988, 135, 325-345. (3) Tummala, R. R. Am. Ceram. Soc. Bull. 1988, 67, 752-758. (4) Rajaram, M.; Friebele, E. J. J. Non-Cryst. Solids 1989, 108, 1-17. (5) Hosono, H.; Abe, Y. J. Non-Cryst. Solids 1995, 190, 185-197. (6) Vogel, J.; Wange, P.; Hartmann, P. Glass Sci. Technol. 1997, 70, 220-223. (7) Massalker, Y.; Sembira, A. N.; Baram, J. J. Mater. Res. 1993, 8, 2445-2457. (8) Larica, C.; Passamani, E. C.; Nunes, E.; Orlando, M. T. D.; Alves, K. M. B. J. Alloys Compd. 1998, 27423-27428. (9) Klugkist, P.; Ratzke, K.; Rehders, S.; Troche, P.; Faupel, F. Phys. ReV. Lett. 1998, 80, 3288-3291. (10) Bunuel, M. A.; Alcala R.; Cases R. Solid State Commun. 1998, 107, 491-495. (11) Franco, R. W. A.; Tambelli, C. C.; Magon, C. J.; Donoso, J. P.; Messaddeq, Y.; Ribeiro, S. J. L.; Poulain, M. J. Chem. Phys. 1998, 109, 2432-2436.
Cheng (12) Dietzel, A. Glass Technol. Ber. 1968, 22, 41-48. (13) Uhlmann, D. R. J. Non-Cryst. Solids 1972, 7, 337-348. (14) Uhlmann, D. R. J. Non-Cryst. Solids 1977, 25, 42-85. (15) Hruby, A.; Czech. J. Phys. B 1972, 22, 1987-1993. (16) Saad, M.; Poulain, M. Mater. Sci. Forum 1987, 19-20, 11-18. (17) Marotta, A.; Buri, A.; Branda, F. J. Non-Cryst. Solids 1987, 9596, 593-600. (18) Zhao, X.; Sakka, S. J. Non-Cryst. Solids 1987, 95-96, 487-494. (19) Branda, F.; Marotta, A.; Buri, A. J. Non-Cryst. Solids 1991, 134, 123-128. (20) Hu, L. L.; Jiang, Z. H. J. Chin. Ceram. Soc. 1990, 18, 315-321. (21) Surinach, S.; Baro, M. D.; Clavaguera-Mora, M. T.; Clavaguera, N. J. Mater. Sci. 1984, 19, 3005-3012. (22) Yang, Q. H.; Jiang, Z. H. J. Chin. Ceram. Soc. 1994, 22, 419425. (23) Dong, D. K.; Bo, Z. L.; Zhu, J. Q. J. Non-Cryst. Solids 1996, 208, 282-287. (24) Avrami, M. J. Chem. Phys. 1939, 7, 177-186. (25) Avrami, M. J. Chem. Phys. 1940, 8, 212-220. (26) Johnson, W. A.; Mehl, F. Trans. Am. Inst. Min. Metall. Eng. 1939, 135, 416-420. (27) West, A. R.; Glasser, F. AdVances in Nucleation and Crystallization in Glasses; The American Ceramic Society: Columbus, OH, 1971; p 151.
